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Today's calculation of Integral 779

Source: 2012 Sophia University entrance exam/Theology, Psychology

February 4, 2012
calculusintegrationconicsparabolaanalytic geometrygeometrycalculus computations

Problem Statement

Consider parabolas Ca:y=−2x2+4ax−2a2+a+1C_a: y=-2x^2+4ax-2a^2+a+1 and C:y=x2−2xC: y=x^2-2x in the coordinate plane. When CaC_a and CC have two intersection points, find the maximum area enclosed by these parabolas.
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